Cremona's table of elliptic curves

574 = 2 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 7- 41-	Signs for the Atkin-Lehner involutions
Class	574j	Isogeny class
Conductor	574	Conductor
∏ cp	5	Product of Tamagawa factors cp
Δ	1621986814 = 2 · 7 · 415	Discriminant
Eigenvalues	2- -1  1 7-  2  4  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-15785,-769911]	[a1,a2,a3,a4,a6]
j	434969885624052241/1621986814	j-invariant
L	2.1296506457988	L(r)(E,1)/r!
Ω	0.42593012915977	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4592h2 18368n2 5166p2 14350d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574j2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-1	1	-	2	4	3	0	4	-5	7	-2	-	-1	-2	-1	10	-13	-2	-3	4	-15	-6	-15	-7

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Quadratic twists for elliptic curve 574j2

-4	8	-3	5	-7	-11	13	41
4592h2	18368n2	5166p2	14350d2	4018n2	69454a2	97006a2	23534t2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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